Since power does increase score yes it could be applied to increasing your score. Probably the fastest way to increase score would be to steal a relic (which will surely get you killed) but it will increase your score by 1k. The safer route to increase score that is a bit safer is to go after crystals that boost your score by 20 each crystal you own. It should also be noted that having crystals does make you a target for larger alliances though.
having a ton of conqs makes you a target aswell BD is a risky game